Exam Name: NSU Paper Name: Number Series Patterns Fundamentals | NSU Question Status: incorrect Correct Marks: 1 Incorrect Marks: N/A Marks Gained: N/A Total Visit Count: 1 Time Spent: 43.522 seconds

Question

Find the next number in the series: 11, 13, 17, 19, 23, ?

Prosyllabus AI · Accepted Answer

Understanding the Problem

You are given the number series:

\[ 11,\ 13,\ 17,\ 19,\ 23,\ ? \]

You selected \(25\), but the correct answer is \(29\).

The fundamental concept you are missing is this:

This is a series of consecutive prime numbers.

Given Data

Series: \(11, 13, 17, 19, 23, ?\)
Options:
- A. \(25\)
- B. \(27\)
- C. \(29\)
- D. \(31\)

What Is a Prime Number?

A prime number is a number greater than \(1\) that has only two factors:

\(1\)
the number itself

Examples of prime numbers:

\[ 2,\ 3,\ 5,\ 7,\ 11,\ 13,\ 17,\ 19,\ 23,\ 29,\ 31,\dots \]

Notice that the given series matches part of this prime-number list.

Step-by-Step Solution

Step 1: Look at the numbers carefully

The series is:

\[ 11,\ 13,\ 17,\ 19,\ 23 \]

All of these are prime numbers.

Step 2: Find the next prime number after \(23\)

Let us check the numbers after \(23\):

\(24\): not prime, because it is divisible by \(2\)
\(25\): not prime, because \(25 = 5 \times 5\)
\(26\): not prime, because it is divisible by \(2\)
\(27\): not prime, because \(27 = 3 \times 9\)
\(28\): not prime, because it is divisible by \(2\)
\(29\): prime

Step 3: Write the next term

So the next number in the series is:

\[ 29 \]

Why \(25\) Is Wrong

You chose \(25\), but:

\[ 25 = 5 \times 5 \]

So \(25\) is not a prime number. Since the pattern is based on prime numbers, \(25\) cannot be the next term.

Another Way to Notice the Pattern

You may have tried looking at the differences:

\[ 13 - 11 = 2,\quad 17 - 13 = 4,\quad 19 - 17 = 2,\quad 23 - 19 = 4 \]

This gives:

\[ +2,\ +4,\ +2,\ +4 \]

If you continue this pattern, you might think the next step is:

\[ 23 + 2 = 25 \]

But this is a trap. In number series, the difference pattern is not always the real rule. Here, the deeper rule is that all terms are consecutive prime numbers.

So always check:

Is it an arithmetic pattern?
Is it squares/cubes?
Is it odd/even?
Is it prime numbers?

Solution Approach for Similar Questions

Check whether the numbers are:
- odd/even
- multiples
- squares or cubes
- prime numbers
Do not rely only on the difference pattern.
Find the simplest and strongest rule that fits all the terms.

Final Answer

\[ \boxed{29} \]

Correct option: C

Key Point to Remember

The missing concept is:

The series contains consecutive prime numbers, not just alternating differences.

Given: